Algebra Examples

$f (x) = 3 x - 2$ , $g (x) = \frac{9}{x + 2}$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (3 x - 2)$ by substituting in the value of $f$ into $g$ .

$g (3 x - 2) = \frac{9}{(3 x - 2) + 2}$

Step 3

Simplify the denominator.

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Step 3.1

Add $- 2$ and $2$ .

$g (3 x - 2) = \frac{9}{3 x + 0}$

Step 3.2

Add $3 x$ and $0$ .

$g (3 x - 2) = \frac{9}{3 x}$

Step 4

Cancel the common factor of $9$ and $3$ .

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Step 4.1

Factor $3$ out of $9$ .

$g (3 x - 2) = \frac{3 \cdot 3}{3 x}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3 x$ .

$g (3 x - 2) = \frac{3 \cdot 3}{3 (x)}$

Step 4.2.2

Cancel the common factor.

$g (3 x - 2) = \frac{3 \cdot 3}{3 x}$

Step 4.2.3

Rewrite the expression.

$g (3 x - 2) = \frac{3}{x}$